Benchmarks for multicomponent diffusion and electrochemical migration

In multicomponent electrolyte solutions, the tendency of ions to diffuse at different rates results in a charge imbalance that is counteracted by the electrostatic coupling between charged species leading to a process called ``electrochemical migration{''} or ``electromigration.{''} Although not commonly considered in solute transport problems, electromigration can strongly affect mass transport processes. The number of reactive transport models that consider electromigration has been growing in recent years, but a direct model intercomparison that specifically focuses on the role of electromigration has not been published to date. This contribution provides a set of three benchmark problems that demonstrate the effect of electric coupling during multicomponent diffusion and electrochemical migration and at the same time facilitate the intercomparison of solutions from existing reactive transport codes. The first benchmark focuses on the 1D transient diffusion of HNO3 (pH = 4) in a NaCl solution into a fixed concentration reservoir, also containing NaCl-but with lower HNO3 concentrations (pH = 6). The second benchmark describes the 1D steady-state migration of the sodium isotope Na-22 triggered by sodium chloride diffusion in neutral pH water. The third benchmark presents a flow-through problem in which transverse dispersion is significantly affected by electromigration. The system is described by 1D transient and 2D steady-state models. Very good agreement on all of the benchmarks was obtained with the three reactive transport codes used: CrunchFlow, MIN3P, and PHREEQC.